One of the most difficult objects in positron emission tomography systems (PET-systems) includes determining the attenuation correction as precisely as possible. Since the gamma quanta, which are generated in the examination object by an interaction between a positron and an electron, pass through the entire region within the detector ring before they are counted by the detector ring, they are attenuated by objects, more particularly by the examination object itself, within the examination region, the so-called field of view (FoV). Hence this attenuation must be corrected in order to obtain images that can be used in a clinical context.
By way of example, this radiation attenuation within an examination object, for example within a human body, can be determined on the basis of a magnetic resonance image. However, a problem here is that the magnetic resonance image or the magnetic resonance signals only weakly correlate with the electron density or the associated linear attenuation coefficients (LAC) of human tissues at the annihilation radiation energy of 511 keV.
In the prior art, as disclosed in, for example, US 2008/135769, it is conventional to produce a magnetic-resonance-based determination of a so-called PET attenuation map by segmenting the magnetic resonance image into different tissue types and assigning appropriate LAC values. Other approaches for a magnetic-resonance-based attenuation correction use a model or a reference image with known attenuation from e.g. a corresponding computed tomography recording or body contours, which are derived from an optical 3D scan. The magnetic resonance image is then combined with the model or the reference image with the known attenuation, and the actual attenuation map is obtained from the combined information.
In further methods, iterative estimation methods are used to obtain simultaneously emission images and attenuation maps from the raw PET data. In the process, use can be made for example of so-called maximum likelihood expectation maximization (MLEM) algorithms, as described in, for example, the following publications:    1) IEEE Trans. Med. Imag., volume 18, p. 393-03, 1999. Simultaneous maximum a posteriori reconstruction of attenuation and activity distributions from emission sinograms, J. Nuyts, S. S. Dupont, R. Benninck, L. Mortelmans, and P. Suetens    2) IEEE Transactions on Medical Imaging, volume 19, number 5, May 2000 451, Reconstructions of Attenuation Map Using Discrete Consistency Conditions, Andrei V. Bronnikov    3) IEEE Transactions of Nuclear Science, volume 54, number 1, February 2007, Activity and Attenuation Reconstruction for Positron Emission Tomography Using Emission Data Only Via Maximum Likelihood and Iterative Data Refinement, Fabiana Crepaldi and Alvaro R. De Pierro
These algorithms usually converge to a local maximum and therefore have to be bounded to achieve the desired solution.
The prior art, as disclosed by Andre Salomon et al. in “Simultaneous Reconstruction of Activity and Attenuation in Multi-Modal ToF-PET” (10th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, pages 339-344), combines a segmentation and a simultaneous reconstruction of the radiation attenuation and the emission image. In the process, the radiation attenuation is not calculated for every pixel; rather, a pre-segmentation of an image on the basis of e.g. a computed tomography image or a magnetic resonance image is used to subdivide the image into segments, and each segment is assigned a linear attenuation coefficient (LAC value) by maximizing the probability of the measured data during the given segmentation and the LAC values assigned to each segment.
In the process, correction factors are calculated and back-projected for the lines of response in order to maximize the probability for each segment in an iterative fashion. Compared to methods based only on a segmentation and assignment of linear attenuation coefficients, this method is able to adapt linear attenuation coefficients individually for each segment rather than basing them on values that, for example, were statistically averaged over a plurality of measurements on different patients. Furthermore, this method makes it possible to determine an attenuation resulting from bones; usually, this is almost impossible in the case of correction methods only based on a magnetic-resonance-based attenuation.